Scaling Properties and Conformal Invariance of the Critical Wave Functions at 2D Anderson Transition in the Spin-Orbit Symmetry Class

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Habibi, Alireza | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43106 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Jafari, Akbar; Saberi, Abbas Ali
Abstract:
In this thesis, first of all we introduce the Anderson model, Multifractality, and conformal field theory. Then we try to determine some critical and scaling quantities for the critical wave functions in the 2D systems with spin-orbit interactions We implement a correction-to-scaling analysis by introducing an irrelevant exponent which leads to a proper and sharp evaluation of the critical parameters including correlation exponent, rescaled localization length and the critical disorder. Then, we survey the multifractal properties of this model and obtain some multifractal exponent in the critical point. Finally, we will survey the existence of the conformal invariance symmetry in it. Our results justify the proposition that the amplitude of the critical wave functions in the SU(2) model behave like a primary field in the conformal field theory which describes the model
Keywords:
Conformal Fields Theory ; Anderson Localization ; Conformal Invariance ; Multifractality ; SU(2) Model ; Finite Size Scaling

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